8192/6561

Interval information

Ratio	8192/6561
Factorization	213 × 3-8
Monzo	[13 -8⟩
Size in cents	384.36¢
Name	Pythagorean diminished fourth
Color name	sw4, sawa 4th
FJS name	[math]\displaystyle{ \text{d4} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	25.6797
Weil norm (log2 max(n, d))	26
Wilson norm (sopfr(nd))	50
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The Pythagorean diminished fourth, 8192/6561, may be reached by subtracting two 81/64 intervals from the perfect octave. It differs from the classic major third, 5/4, by the schisma (around 2 cents), and, as a result, the Pythagorean diminished fourth is in fact rather consonant. According to Aura, while 8192/6561 may take the place of the classic major third in chords, its status as a diminished fourth means that it has a different function in terms of voice-leading.

Due to 8192/6561's extreme proximity to 5/4, some may consider it a major third (see Extended-diatonic interval names).

See also

• 6561/4096 – its octave complement
• 19683/16384 – its fifth complement
• Gallery of just intervals
• Pythagorean tuning